Do we need to balance the turn order advantage?

[stevegrossi]

As part of #15, I'm working on an "AI Arena" where I can have AIs play games against each other in order to help me gauge whether a particular AI algorithm is any better than the last. The thing is, when I tried to establish a baseline, it looks like, at least for the AI but possibly for human players as well, going earlier in the turn order bestows a significant advantage, with the first player nearly twice as likely to win as the last.

Each run of mix ai.arena here spins up 1,000 games (4 identical AI players on the Japan map), all of which complete in under 5 seconds (pretty cool 😎 ):

$ mix ai.arena
Player | Win %
-------|------
 1     | 0.333
 2     | 0.292
 3     | 0.198
 4     | 0.177

$ mix ai.arena
Player | Win %
-------|------
 1     | 0.326
 2     | 0.26
 3     | 0.228
 4     | 0.186

$ mix ai.arena
Player | Win %
-------|------
 1     | 0.309
 2     | 0.275
 3     | 0.219
 4     | 0.197

[stevegrossi]

Ooh! I've been interested in the AI.Arena again and tried it on some of the new maps. Wheel and Europe both replicate the significant (nearly 2x) advantage to the player who goes first vs. the one who goes last, but interestingly the Westeros map leads to nearly even results!

> mix ai.arena
Player | Win %
-------|-------
     1 |  12.6%
     2 |  13.4%
     3 |  13.0%
     4 |  11.1%
     5 |  11.0%
     6 |  13.2%
     7 |  13.5%
     8 |  12.0%
   Tie |   0.2%

Maybe there's something about that old Iron Throne that gives everyone a fair shot at it... 🤔

[yakryder]

Maybe we could start checking results with giving the first player one or more fewer units on one or more turns.

[yakryder]

Also you may have already read this, but:

Correcting for the first-player advantage in Risk